Details

Time bar (total: 3.1s)

analyze422.0ms (13.6%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
21.8%78%0.1%7
26.5%73.3%0.1%8
36.7%63.2%0.1%9
41.3%49.9%8.7%10
47.2%43.3%9.5%11
54.4%35.5%10.1%12
57.9%27.4%14.7%13
61.7%23.2%15.1%14
Compiler

Compiled 8 to 8 computations (0% saved)

sample31.0ms (1%)

Algorithm
1×intervals
Results
12.0ms256×body128valid
1.0ms13×body128invalid
Compiler

Compiled 15 to 18 computations (-20% saved)

simplify154.0ms (5%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (7.0ms)

IterNodesCost
010410
110410

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.0b
Counts
2 → 1
Compiler

Compiled 14 to 14 computations (0% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.0b
(*.f64 (+.f64 x y) (+.f64 z 1))

rewrite12.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
7×*-un-lft-identity_binary64_419
6×flip3-+_binary64_422 flip-+_binary64_393
5×add-sqr-sqrt_binary64_441
4×associate-*r*_binary64_359 frac-times_binary64_429 associate-*l*_binary64_360
3×add-cube-cbrt_binary64_454 add-cbrt-cube_binary64_455 add-exp-log_binary64_457 pow1_binary64_480
2×associate-*l/_binary64_362 distribute-lft-out_binary64_370 associate-*r/_binary64_361
1×pow-prod-down_binary64_490 add-log-exp_binary64_458 distribute-rgt-in_binary64_369 unswap-sqr_binary64_387 prod-exp_binary64_468 cbrt-unprod_binary64_452 distribute-lft-in_binary64_368 *-commutative_binary64_350
Counts
1 → 30
Calls

1 calls:

10.0ms
(*.f64 (+.f64 x y) (+.f64 z 1))

series42.0ms (1.3%)

Counts
1 → 3
Calls

1 calls:

42.0ms
(*.f64 (+.f64 x y) (+.f64 z 1))

simplify94.0ms (3%)

Algorithm
1×egg-herbie
Counts
33 → 33
Iterations

Useful iterations: 0 (77.0ms)

IterNodesCost
04963502
14963502

prune53.0ms (1.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New30333
Fresh000
Picked011
Done000
Total30434
Error
0b
Counts
34 → 4
Compiler

Compiled 495 to 251 computations (49.3% saved)

localize10.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b
(+.f64 (*.f64 (+.f64 x y) z) (+.f64 x y))
0.0b
(*.f64 (+.f64 x y) z)

rewrite30.0ms (1%)

Algorithm
1×rewrite-expression-head
Rules
7×add-log-exp_binary64_458
6×flip3-+_binary64_422 *-un-lft-identity_binary64_419 associate-*l/_binary64_362 add-sqr-sqrt_binary64_441 flip-+_binary64_393
4×frac-add_binary64_427 add-cube-cbrt_binary64_454 associate-*l*_binary64_360 add-cbrt-cube_binary64_455 add-exp-log_binary64_457 pow1_binary64_480
3×associate-*r*_binary64_359 sum-log_binary64_510
1×associate-+r+_binary64_351 pow-prod-down_binary64_490 unswap-sqr_binary64_387 prod-exp_binary64_468 cbrt-unprod_binary64_452 distribute-lft-out_binary64_370 *-commutative_binary64_350 +-commutative_binary64_349
Counts
2 → 38
Calls

2 calls:

15.0ms
(+.f64 (*.f64 (+.f64 x y) z) (+.f64 x y))
12.0ms
(*.f64 (+.f64 x y) z)

series81.0ms (2.6%)

Counts
2 → 6
Calls

2 calls:

58.0ms
(+.f64 (*.f64 (+.f64 x y) z) (+.f64 x y))
23.0ms
(*.f64 (+.f64 x y) z)

simplify87.0ms (2.8%)

Algorithm
1×egg-herbie
Counts
44 → 44
Iterations

Useful iterations: 0 (67.0ms)

IterNodesCost
05041674

prune41.0ms (1.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New44044
Fresh022
Picked011
Done011
Total44448
Error
0b
Counts
48 → 4
Compiler

Compiled 705 to 231 computations (67.2% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b
(*.f64 (+.f64 z 1) (sqrt.f64 (+.f64 x y)))
0.2b
(*.f64 (sqrt.f64 (+.f64 x y)) (*.f64 (+.f64 z 1) (sqrt.f64 (+.f64 x y))))

rewrite49.0ms (1.6%)

Algorithm
1×rewrite-expression-head
Rules
42×sqrt-div_binary64_436
33×flip3-+_binary64_422 flip-+_binary64_393
32×frac-times_binary64_429
16×associate-*r/_binary64_361
13×*-un-lft-identity_binary64_419
11×add-sqr-sqrt_binary64_441 associate-*l*_binary64_360
10×associate-*l/_binary64_362
9×add-cbrt-cube_binary64_455 add-exp-log_binary64_457 sqrt-prod_binary64_435 pow1_binary64_480
8×associate-*r*_binary64_359
7×add-cube-cbrt_binary64_454
4×pow-prod-down_binary64_490 prod-exp_binary64_468 cbrt-unprod_binary64_452
3×distribute-lft-out_binary64_370
2×add-log-exp_binary64_458 unswap-sqr_binary64_387 *-commutative_binary64_350
Counts
2 → 80
Calls

2 calls:

18.0ms
(*.f64 (sqrt.f64 (+.f64 x y)) (*.f64 (+.f64 z 1) (sqrt.f64 (+.f64 x y))))
12.0ms
(*.f64 (+.f64 z 1) (sqrt.f64 (+.f64 x y)))

series120.0ms (3.9%)

Counts
2 → 6
Calls

2 calls:

80.0ms
(*.f64 (+.f64 z 1) (sqrt.f64 (+.f64 x y)))
39.0ms
(*.f64 (sqrt.f64 (+.f64 x y)) (*.f64 (+.f64 z 1) (sqrt.f64 (+.f64 x y))))

simplify93.0ms (3%)

Algorithm
1×egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
049631996
149631996

prune106.0ms (3.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New86086
Fresh011
Picked011
Done022
Total86490
Error
0b
Counts
90 → 4
Compiler

Compiled 1888 to 761 computations (59.7% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b
(*.f64 (-.f64 z 1) (-.f64 x y))
2.5b
(-.f64 (*.f64 x x) (*.f64 y y))
5.3b
(*.f64 (-.f64 (*.f64 z z) 1) (-.f64 (*.f64 x x) (*.f64 y y)))
32.8b
(/.f64 (*.f64 (-.f64 (*.f64 z z) 1) (-.f64 (*.f64 x x) (*.f64 y y))) (*.f64 (-.f64 z 1) (-.f64 x y)))

rewrite68.0ms (2.2%)

Algorithm
1×rewrite-expression-head
Rules
25×flip3--_binary64_423 flip--_binary64_394
21×add-sqr-sqrt_binary64_441
20×add-cbrt-cube_binary64_455 add-exp-log_binary64_457
16×*-un-lft-identity_binary64_419 frac-times_binary64_429
13×associate-*l*_binary64_360
10×add-cube-cbrt_binary64_454
9×associate-*r*_binary64_359 cancel-sign-sub-inv_binary64_385
8×associate-*l/_binary64_362 associate-*r/_binary64_361 associate-/r/_binary64_365 pow1_binary64_480 associate-/l/_binary64_366
7×difference-of-squares_binary64_388
6×add-log-exp_binary64_458 distribute-rgt-in_binary64_369 prod-exp_binary64_468 cbrt-unprod_binary64_452 distribute-lft-in_binary64_368
5×sub-neg_binary64_412
4×div-exp_binary64_470 cbrt-undiv_binary64_453
2×pow-prod-down_binary64_490 difference-of-sqr-1_binary64_389 unswap-sqr_binary64_387 distribute-lft-out--_binary64_371 *-commutative_binary64_350
1×clear-num_binary64_418 times-frac_binary64_425 div-inv_binary64_416 frac-2neg_binary64_430 diff-log_binary64_511 associate-/r*_binary64_363 associate-/l*_binary64_364
Counts
4 → 124
Calls

4 calls:

19.0ms
(/.f64 (*.f64 (-.f64 (*.f64 z z) 1) (-.f64 (*.f64 x x) (*.f64 y y))) (*.f64 (-.f64 z 1) (-.f64 x y)))
17.0ms
(*.f64 (-.f64 z 1) (-.f64 x y))
13.0ms
(*.f64 (-.f64 (*.f64 z z) 1) (-.f64 (*.f64 x x) (*.f64 y y)))
7.0ms
(-.f64 (*.f64 x x) (*.f64 y y))

series368.0ms (11.8%)

Counts
4 → 12
Calls

4 calls:

199.0ms
(/.f64 (*.f64 (-.f64 (*.f64 z z) 1) (-.f64 (*.f64 x x) (*.f64 y y))) (*.f64 (-.f64 z 1) (-.f64 x y)))
99.0ms
(*.f64 (-.f64 (*.f64 z z) 1) (-.f64 (*.f64 x x) (*.f64 y y)))
38.0ms
(-.f64 (*.f64 x x) (*.f64 y y))
32.0ms
(*.f64 (-.f64 z 1) (-.f64 x y))

simplify107.0ms (3.4%)

Algorithm
1×egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 0 (71.0ms)

IterNodesCost
049912519
149912519

prune180.0ms (5.8%)

Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New1360136
Fresh000
Picked011
Done033
Total1364140
Error
0b
Counts
140 → 4
Compiler

Compiled 3552 to 1441 computations (59.4% saved)

regimes171.0ms (5.5%)

Accuracy

Total 0.0b remaining (75.4%)

Threshold costs 0.0b (75.4%)

Compiler

Compiled 717 to 598 computations (16.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01013
11013

end0.0ms (0%)

sample757.0ms (24.4%)

Algorithm
1×intervals
Results
279.0ms7999×body128valid
22.0ms599×body128invalid
0.0ms1×body1024valid
Compiler

Compiled 126 to 103 computations (18.3% saved)

Profiling

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